Branched shadows and complex structures of 4-manifolds

2005/02/14 by Francesco Costantino, Costantino, Francesco
Computer Science · Mathematics · #32C60 #57M20 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.DG #math.GT #msc:32C60 #msc:57M20

paper · pdf · doi:10.48550/arxiv.math/0502292

24 pages, 9 figures

arxiv created 2005/02/14 · openalex publication_date 2005/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spin^c-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-handlebody is homotopic to a complex one.

Related

• A short introduction to shadows of 4-manifolds
• Four-manifolds with shadow-complexity one
• Shadow-complexity and trisection genus
• Presentation of the fundamental groups of complements of shadows
• Constructing Combinatorial 4-Manifolds